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In this Note, the relative motion between two spacecraft is studied with emphasis on physical insights. The full equations of relative motion in Keplerian orbits are converted into the general form of a second-order differential e...
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In this Note, the relative motion between two spacecraft is studied with emphasis on physical insights. The full equations of relative motion in Keplerian orbits are converted into the general form of a second-order differential equation, and then feedback control laws are proposed for different control objectives. Besides the control laws presented in this Note, other various control design methods, which have already been developed for other applications (such as robot manipulator or spacecraft control), can also be easily applied for the relative motion control, thanks to the use of the generic form.
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On the basis of a noninfinitesimal deviation vector a new derivation (in spaces with the affine connection) of a generalized deviation is given for the case when the curves appearing in it, which can be geodesic as well as nongeod...
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On the basis of a noninfinitesimal deviation vector a new derivation (in spaces with the affine connection) of a generalized deviation is given for the case when the curves appearing in it, which can be geodesic as well as nongeodesic, are given implicitly (by second order differential equations). It is shown that the equations of relative motion of two point particles in spaces with the affine connection in the field of external forces are special cases of the generalized deviation equation. As examples the ''Euclidean case'' and the general infinitesimal (local) deviation equation are considered. 6 refs. (Atomindex citation 19:037165)
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Investigations under the Contract have mainly been in two categories: the classical theory of the ellipsoidal figures of equilibrium and the development of a post-Newtonian theory of hydrodynamics in the framework of general relat...
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Investigations under the Contract have mainly been in two categories: the classical theory of the ellipsoidal figures of equilibrium and the development of a post-Newtonian theory of hydrodynamics in the framework of general relativity. A complete list of publications under the contract, is given.
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The equations of motion of a dynamical system are discussed in terms of the initial data. The point of view emphasized is that the initial data are explicitly time dependent constants of the motion, knowledge of which constitutes,...
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The equations of motion of a dynamical system are discussed in terms of the initial data. The point of view emphasized is that the initial data are explicitly time dependent constants of the motion, knowledge of which constitutes, implicitly, a complete solution of the equations. A general algorithm for constructing the set of constants in this form and from it, the complete solution, is given. The algorithm provides a complete, formal solution for the dynamical equations in terms of the Hamiltonian function. (Author)
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The action for the classical model of the electron exhibiting Zitterbewegung is generalized to curved space by introducing a spin connection. The dynamical equations and the symplectic structure are given for several different cho...
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The action for the classical model of the electron exhibiting Zitterbewegung is generalized to curved space by introducing a spin connection. The dynamical equations and the symplectic structure are given for several different choices of the variables. In particular, we obtain the equation of motion for spin and compare it with the Papapetrou equation. 18 refs. (Atomindex citation 18:062444)
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An important aspect of qualitative spatial reasoning is understanding mechanisms. This paper presents a qualitative analysis of motion for mechanical linkages. In particular, we describe how to analyze the behavior of a mechanism ...
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An important aspect of qualitative spatial reasoning is understanding mechanisms. This paper presents a qualitative analysis of motion for mechanical linkages. In particular, we describe how to analyze the behavior of a mechanism which has a movable axis. The basic idea of our approach is to represent relative motions of the link in terms of quadrants (qualitatively representing the direction relative to a global reference frame) and relative inclinations relative to the x-axis. Using this representation ; we can derive all the possible motions of a system of linkages. This idea has been implemented and tested on several examples.
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We show that a generalized (or power law ) inflationary phase arises naturally and inevitably in a simple (Bianchi Type I) anisotropic cosmological model in the self-consistent Einstein-Cartan gravitation theory with the improved ...
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We show that a generalized (or power law ) inflationary phase arises naturally and inevitably in a simple (Bianchi Type I) anisotropic cosmological model in the self-consistent Einstein-Cartan gravitation theory with the improved stress-energy-momentum tensor with spin density of Ray and Smalley. This is made explicit by analytical solution of the field equations of motion of the fluid variables. The inflation is caused by the angular kinetic energy density due to spin. The model further elucidates the relationship between fluid vorticity, the angular velocity of the inertially-dragged tetrads, and the precession of the principal axes of the shear ellipsoid. Shear is not effective in damping the inflation. (Author).
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An aether-based treatment of space and time measurement is employed toinvestigate the rate of a moving clock, to develop doppler formulae, and to establish intra and inter-frame relationships in electrodynamics.
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The rotational laws of motion for arbitrarily shaped, weakly self-gravitatingbodies, members of gravitationally interacting N-body systems, are obtained at the first post-Newtonian approximation of general relativity. The derivati...
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The rotational laws of motion for arbitrarily shaped, weakly self-gravitatingbodies, members of gravitationally interacting N-body systems, are obtained at the first post-Newtonian approximation of general relativity. The derivation uses our previously introduced framework, characterized by the combined use of N local (body-attached) reference systems with one global reference system, and by the introduction of new sets of relativistic multipole moments, and relativistic tidal moments. The authors show how to associate to each body (considered in its corresponding local frame) a first-post-Newtonian-accurate spin vector, whose local-time evolution is entirely determined by the coupling between the multipole moments of that body and the tidal moments it experiences. The leading relativistic effects in the spin motion are discussed: gravitational Larmor theorem (De Sitter-Fokker-Eddington precession) and post-Newtonian contributions to the torque associated to the quadrupole moment and the quadrupole tidal tensor.
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